Question: Simplify the following expression: $r = \dfrac{-4a^2 + 16a - 12}{a - 1} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ r =\dfrac{-4(a^2 - 4a + 3)}{a - 1} $ Then we factor the remaining polynomial: $a^2 {-4}a + {3} $ ${-1} {-3} = {-4}$ ${-1} \times {-3} = {3}$ $ (a {-1}) (a {-3}) $ This gives us a factored expression: $\dfrac{-4(a {-1}) (a {-3})}{a - 1}$ We can divide the numerator and denominator by $(a + 1)$ on condition that $a \neq 1$ Therefore $r = -4(a - 3); a \neq 1$